Finite depth effects on solitary waves in a floating ice sheet

A theoretical and numerical study of two-dimensional nonlinear flexural-gravity waves propagating at the surface of an ideal fluid of finite depth, covered by a thin ice sheet, is presented. The ice-sheet model is based on the special Cosserat theory of hyperelastic shells satisfying Kirchhoff׳s hypothesis, which yields a conservative and nonlinear expression for the bending force. From a Hamiltonian reformulation of the governing equations, two weakly nonlinear wave models are derived: a 5th-order Korteweg–de Vries equation in the long-wave regime and a cubic nonlinear Schrödinger equation in the modulational regime. Solitary wave solutions of these models and their stability are analysed. In particular, there is a critical depth below which the nonlinear Schrödinger equation is of focusing type and thus admits stable soliton solutions. These weakly nonlinear results are validated by comparison with direct numerical simulations of the full governing equations. It is observed numerically that small- to large-amplitude solitary waves of depression are stable. Overturning waves of depression are also found for low wave speeds and sufficiently large depth. However, solitary waves of elevation seem to be unstable in all cases

Water wave transmission by an array of floating disks

An experimental validation of theoretical models of transmission of regular water waves by large arrays of floating disks is presented. The experiments are conducted in a wave basin. The models are based on combined potential-flow and thin-plate theories, and the assumption of linear motions. A low-concentration array, in which disks are separated by approximately a disk diameter in equilibrium, and a high-concentration array, in which adjacent disks are almost touching in equilibrium, are used for the experiments. The proportion of incident wave energy transmitted by the disks is presented as a function of wave period, and for different wave amplitudes. Results indicate that the models predict wave energy transmission accurately for small-amplitude waves and low-concentration arrays. Discrepancies for large-amplitude waves and high-concentration arrays are attributed to wave overwash of the disks and collisions between disks. Validation of model predictions of rigid-body motions of a solitary disk are also presented

Sea ice thickness from air-coupled flexural waves

Air-coupled flexural waves (ACFWs) appear as wave trains of constant frequency that arrive in advance of the direct air wave from an impulsive source travelling over a floating ice sheet. The frequency of these waves varies with the flexural stiffness of the ice sheet, which is controlled by a combination of thickness and elastic properties. We develop a theoretical framework to understand these waves, utilizing modern numerical and Fourier methods to give a simpler and more accessible description than the pioneering yet unwieldy analytical efforts of the 1950s. Our favoured dynamical model can be understood in terms of linear filter theory and is closely related to models used to describe the flexural waves produced by moving vehicles on floating plates. We find that air-coupled flexural waves are a real and measurable component of the total wave field of floating ice sheets excited by impulsive sources, and we present a simple closed-form estimator for the ice thickness based on observable properties of the air-coupled flexural waves. Our study is focused on first-year sea ice of ∼ 20–80 cm thickness in Van Mijenfjorden, Svalbard, that was investigated through active source seismic experiments over four field campaigns in 2013, 2016, 2017 and 2018. The air-coupled flexural wave for the sea ice system considered in this study occurs at a constant frequency thickness product of ∼ 48 Hz m. Our field data include ice ranging from ∼ 20–80 cm thickness with corresponding air-coupled flexural frequencies from 240 Hz for the thinnest ice to 60 Hz for the thickest ice. While air-coupled flexural waves for thick sea ice have received little attention, the readily audible, higher frequencies associated with thin ice on freshwater lakes and rivers are well known to the ice-skating community and have been reported in popular media. The results of this study and further examples from lake ice suggest the possibility of non-contact estimation of ice thickness using simple, inexpensive microphones located above the ice sheet or along the shoreline. While we have demonstrated the use of air-coupled flexural waves for ice thickness monitoring using an active source acquisition scheme, naturally forming cracks in the ice are also shown as a potential impulsive source that could allow passive recording of air-coupled flexural waves

Microphone recording of flexural waves for estimation of lake ice thickness

In this study we took an intentionally low-tech approach, aiming to estimate key physical parameters of lake ice using a single, inexpensive microphone. We consider this approach highly relevant to the issue of transport safety and the relatively high number of accidents involving breakthrough failure of thin ice underlines the importance of this topic. We conducted a range of experiments on three frozen lakes in the Tromsø region of Northern Norway and found that the monochromatic air-coupled flexural wave was a robust feature of impulsively excited frozen lakes. Ice thickness was estimated via a closed form solution that only depends on the measured monochromatic frequency of the air-coupled flexural wave and a set of assumed physical parameters for the ice, air and water. We discuss the impact of uncertainty in the assumed parameters on estimated ice thickness and bearing capacity, finding the uncertainty to be quite small, particularly when physical observation of ice type or drilled thickness are available to constrain the assumed Young’s modulus of the ice. Ice thicknesses estimated from air-coupled flexural waves were typically within 5–10% of ice thickness measured in holes drilled in the vicinity of the microphone for both artificial sources including hammer strikes, jumping and tapping with ice skates and natural ice quakes. The thickness estimates were also similarly accurate whether the microphone was resting on the ice, placed on land along the shoreline or handheld. We also showed that it is possible to record the dispersive ice flexural wave using a microphone, particularly when it was resting on the ice surface. Since thickness was constrained by the air-coupled flexural wave, we were able to estimate the propagation distance, corresponding to the horizontal offset between source and microphone, by inversion of the time dispersed arrival of the chirp signal corresponding to the ice flexural wave. We also demonstrated that a microphone can record inharmonic monochromatic overtones of the air-coupled flexural wave, that were linked to the geometry and boundary conditions of the frozen lakes using finite element modal analysis. This study leads us to conclude that a simple microphone can be a powerful tool giving a surprising amount of information on the lake-ice system. Using a microphone to record air-coupled flexural waves appears to be a promising additional tool for evaluation of ice conditions, convenient enough that it could substantially increase the availability of timely and accurate information on ice thickness and thereby contribute to safer travel on floating ice

Seasonal and spatial variations in the ocean-coupled ambient wavefield of the Ross Ice Shelf

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Baker, M. G., Aster, R. C., Anthony, R. E., Chaput, J., Wiens, D. A., Nyblade, A., Bromirski, P. D., Gerstoft, P., & Stephen, R. A. Seasonal and spatial variations in the ocean-coupled ambient wavefield of the Ross Ice Shelf. Journal of Glaciology, 65(254), (2019): 912-925, doi:10.1017/jog.2019.64.The Ross Ice Shelf (RIS) is host to a broadband, multimode seismic wavefield that is excited in response to atmospheric, oceanic and solid Earth source processes. A 34-station broadband seismographic network installed on the RIS from late 2014 through early 2017 produced continuous vibrational observations of Earth's largest ice shelf at both floating and grounded locations. We characterize temporal and spatial variations in broadband ambient wavefield power, with a focus on period bands associated with primary (10–20 s) and secondary (5–10 s) microseism signals, and an oceanic source process near the ice front (0.4–4.0 s). Horizontal component signals on floating stations overwhelmingly reflect oceanic excitations year-round due to near-complete isolation from solid Earth shear waves. The spectrum at all periods is shown to be strongly modulated by the concentration of sea ice near the ice shelf front. Contiguous and extensive sea ice damps ocean wave coupling sufficiently so that wintertime background levels can approach or surpass those of land-sited stations in Antarctica.This research was supported by NSF grants PLR-1142518, 1141916, 1142126, 1246151 and 1246416. JC was additionally supported by Yates funds in the Colorado State University Department of Mathematics. PDB also received support from the California Department of Parks and Recreation, Division of Boating and Waterways under contract 11-106-107. We thank Reinhard Flick and Patrick Shore for their support during field work, Tom Bolmer in locating stations and preparing maps, and the US Antarctic Program for logistical support. The seismic instruments were provided by the Incorporated Research Institutions for Seismology (IRIS) through the PASSCAL Instrument Center at New Mexico Tech. Data collected are available through the IRIS Data Management Center under RIS and DRIS network code XH. The PSD-PDFs presented in this study were processed with the IRIS Noise Tool Kit (Bahavar and others, 2013). The facilities of the IRIS Consortium are supported by the National Science Foundation under Cooperative Agreement EAR-1261681 and the DOE National Nuclear Security Administration. The authors appreciate the support of the University of Wisconsin-Madison Automatic Weather Station Program for the data set, data display and information; funded under NSF grant number ANT-1543305. The Ross Ice Shelf profiles were generated using the Antarctic Mapping Tools (Greene and others, 2017). Regional maps were generated with the Generic Mapping Tools (Wessel and Smith, 1998). Topography and bathymetry data for all maps in this study were sourced from the National Geophysical Data Center ETOPO1 Global Relief Model (doi:10.7289/V5C8276M). We thank two anonymous reviewers for suggestions on the scope and organization of this paper

Proceedings of the 39th International Workshop on Water Waves and Floating Bodies

The International Workshop on Water Waves and Floating Bodies (IWWWFB) is anannual meeting of engineers and scientists with a particular emphasis on waterwaves and their effects on floating and fixed marine structures. The Workshop wasinitiated by Professor D. V. Evans (University of Bristol) and Professor J. N. Newman(MIT) following informal meetings between their research groups in 1984. Firstintended to promote communication between researchers in the UK and the USA,the interest and participation quickly spread to include researchers from many othercountries around the world.The Workshop enhances the basic and applied scientific knowledge on water wavesand their interaction with floating and fixed bodies with various applications andfacilitates the advancement and transfer of knowledge between research groupsacross the globe, and between senior and early career researchers. The workshopproceedings are freely accessible through the dedicated internet addresswww.iwwwfb.org where all contributions from 1986 on can be found.Individual papers from the 2024 conference can be found on the IWWWFB website here: http://www.iwwwfb.org/Workshops/39.htm 

Proceedings of the 39th International Workshop on Water Waves and Floating Bodies

The International Workshop on Water Waves and Floating Bodies (IWWWFB) is anannual meeting of engineers and scientists with a particular emphasis on waterwaves and their effects on floating and fixed marine structures. The Workshop wasinitiated by Professor D. V. Evans (University of Bristol) and Professor J. N. Newman(MIT) following informal meetings between their research groups in 1984. Firstintended to promote communication between researchers in the UK and the USA,the interest and participation quickly spread to include researchers from many othercountries around the world.The Workshop enhances the basic and applied scientific knowledge on water wavesand their interaction with floating and fixed bodies with various applications andfacilitates the advancement and transfer of knowledge between research groupsacross the globe, and between senior and early career researchers. The workshopproceedings are freely accessible through the dedicated internet addresswww.iwwwfb.org where all contributions from 1986 on can be found.Individual papers from the 2024 conference can be found on the IWWWFB website here: http://www.iwwwfb.org/Workshops/39.htm